Anatomy of the ρ resonance from lattice QCD at the physical point

Journal Article · Fri Apr 27 00:00:00 EDT 2018 · Chinese Physics. C, High Energy Physics and Nuclear Physics

DOI:https://doi.org/10.1088/1674-1137/42/6/063102· OSTI ID:1506458

Sun, Wei ^[1]; Alexandru, Andrei ^[2]; Chen, Ying ^[1]; Draper, Terrence ^[3]; Liu, Zhaofeng ^[1]; Yang, Yi -Bo ^[4]

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1. Chinese Academy of Sciences (CAS), Beijing (China)
2. George Washington Univ., Washington, DC (United States)
3. Univ. of Kentucky, Lexington, KY (United States)
4. Michigan State Univ., East Lansing, MI (United States)

We propose a strategy to access the $$q\bar{q}$$ component of the ρ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the $$q\bar{q}$$ component is derived at different valence quark masses, and shows a linear dependence on $${m}_{{\rm{\pi }}}^{2}$$. The slope is determined to be $${c}_{1}=0.505(3)\,{{\rm{GeV}}}^{-1}$$, from which the valence $${\rm{\pi }}{\rm{\rho }}$$ sigma term is extracted to be $${\sigma }_{{\rm{\pi }}{\rm{\rho }}}^{(\mathrm{val})}=9.82(6)$$ MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the $$q\bar{q}$$ component is interpolated to be $${m}_{{\rm{\rho }}}=775.9\pm 6.0\pm 1.8\,{\rm{MeV}}$$, which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the $$q\bar{q}$$ component to be $${f}_{{{\rm{\rho }}}^{-}}=208.5\pm 5.5\pm 0.9\,{\rm{MeV}}$$, which can be compared with the experimental value $${f}_{{\rm{\rho }}}^{{\rm{\exp }}}\approx 221\,{\rm{MeV}}$$ through the relation $${f}_{{\rm{\rho }}}^{{\rm{\exp }}}=\sqrt{{Z}_{{\rm{\rho }}}}{f}_{{{\rm{\rho }}}^{\pm }}$$, with $${Z}_{{\rm{\rho }}}\approx 1.13$$ being the on-shell wavefunction renormalization of ρ owing to the $${\rm{\rho }}-{\rm{\pi }}$$ interaction. We emphasize that $${m}_{{\rm{\rho }}}$$ and $${f}_{{\rm{\rho }}}$$ of the $$q\bar{q}$$ component, which are obtained for the first time from QCD, can be taken as the input parameters of ρ in effective field theory studies where ρ acts as a fundamental degree of freedom.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); George Washington Univ., Washington, DC (United States); Univ. of Kentucky, Lexington, KY (United States); UT-Battelle LLC/ORNL, Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Contributing Organization: χQCD Collaboration
• Grant/Contract Number: FG02-95ER40907; SC0013065; AC05-00OR22725
• OSTI ID: 1506458
• Journal Information: Chinese Physics. C, High Energy Physics and Nuclear Physics, Vol. 42, Issue 6; ISSN 1674-1137
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ρ resonance
leptonic decay constant
renormalization